2748
H3P+ could exist over only a very limited pH range. This conclusion has since been verified for protoporphyrin62 in aqueous hydrochloric acid solutions, where it was found that, within the experimental error of the method of continuous variations, the two protons added simultaneously. AronoffB3later found, however, that upon titration of several porphyrins with perchloric acid in nitrobenzene, a distinct spectrum assumed to be that of the monocation was found for some porphyrins, while such a spectrum was totally absent for others. He also listed a third class of porphyrins, including tetraphenylporphine, for which an intermediate spectrum was indicated by small shifts in isosbestic points. Even in the cases where an intermediate spectrum was detected, however, KZ was calculated to be at least three times greater than Kl. It should be mentioned that while the monosalts have never been isolated, there is now sufficient spectral evidence supporting their existence in anionic detergents, which evidently stabilize the singly charged species with respect to the free base. There has been no conclusive proof that the monocations exist in detectable concentrations in aqueous solutions, although Neuberger and Scott5j have presented spectra of what they claim to be the monoacids of a number of porphyrins in buffered, aqueous solutions. However, their results have been questioned because of their use of buffer solutions containing alkali ions and because the porphyrins they used contained carboxylic and sulfonic acid groups, whose pK's are in the pH range at which the supposed monocations appeared. A careful study of porphyrin free base-diacid equilibria was undertaken on the water-soluble H2TPyPz4
system. Excellent isosbestic points were obtained upon changing the pH of an aqueous hydrochloric acid solution from 2.30, at which point 98% of the porphyrin is in the free base form, to 0.00, where essentially all of the porphyrin is in the diacid form. In addition, the observed change in optical density was quantitatively consistent with the single equilibrium H4TPyPz+)c H2TPyP
+ 2H+
K = KiK2
A value of 5.4 X
(moles/l.)2 was reported for K . Thus, the bulk of the experimental evidence indicates that the second proton is added (or abstracted) much more easily than the first. This, of course, is contrary to what is found for most dibasic acids, in which successive proton transfers occur with increasing difficulty as a result of the accumulating charge. The relative instability of the monoacid had previously been explained solely in terms of the loss of symmetry, which decreased the resonance stabilization. Undoubtedly, this factor is important, and perhaps, even predominant in reducing the relative stability of the monoacid. However, the nonplanar configuration found in the diacids affords a second explanation. The energy barrier for the addition of the first proton may be greater than that for the addition of the second, because the first proton attacks a relatively planar molecule, with lone-pair electrons on the unprotonated nitrogens directed toward the center of the ring, a sterically unfavorable location. Upon incorporation of the first proton to form the monoacid, the pyrrole rings are probably tilted up and down as in the diacid, so that the opposite nitrogen's nonbonding electron pair is quite accessible to attack by a second proton.64 (64) This research was partly supported by the grants from the NIH,
(62) R. I. Walter, J . Am. Chem. SOC.,75, 3860 (1953). (63) S . Aronoff, J . Phys. Chem., 62, 428 (1958).
ARPA, and NSF.
The Crystal and Molecular Structure of Octahydroxycy clobutane C . M. Bock Contribution from the Air Force Rocket Propulsion Laboratory, Air Force Systems Command, Edwards, California. Received December 26, 36 AbtraFt: OctahydrFxycyclobutanecrystallizes in the monoclinic system P21/n, = 7.525 A,bo = 5.472 A,co = 7.491 A (all =t0.005 A), 6 = 90.00 & 0.05 '. The structure was solved by the symbolic addition method. The two molecules in the unit cell lie on centersoofsymmetry and thus require the cyclobutane ring to be planar. The average carbon-oxygen bond length is 1.385 A and the carbon-carbon bond length is 1.562 A. The average 0-C-0 bond angle is 111.8'. The structure is held together by a loose three-dimensional network of hydrogen bonds involving all of the hydroxyls in the system.
he synthesis of the novel compound octahydroxycyclobutane was first reported by West, Niu, and Itol in 1963. The original workers on the compound predicted a planar structure for the cyclobutane ring on the basis of infrared data; however, the possibility of slight torsional deformation was not ruled out.
T
(1) R. West, H. Y . Niu, and M. Ito, J. Am. Chem. Soc., 85, 2584 (1963).
Journal of the American Chemical Society
1
90:11
The variability of conformation in cyclobutane rings has been reviewed by Lambert and Roberts,2 and from their work it would seem that there is no a priori way of predicting the conformation of the ring skeleton after substitution. The purpose of this study is to establish exactly the conformation of this molecular structure*
/ May 22, 1968
(2) J. R. Lambert and J. D. Roberts, ibid., 87. 3884 (1965).
2749 Table I. Statistical Data for the Distribution of Normalized Structure Factors Observed
Theoretical for centrosymmetric
Noncentrosymmetric
1.OO 0.798 0.968
1 .oo 0.886 0.736
lE12 = 1.02 IEl = 0.735 lEI2 - 1 = 1.06
.”
where S means “sign of From an initial uzlisting, 16 additional signs were developed relying o n the probability relationships
P
E
325 -715 3 34 2_18 802 433
3.16 3.27 2.66 3.01 2.87 2.68
Q31
1 EZET;-i;
EF, i;
where an = Z j m l N Z p , 2,being the atomic number of the jth atom in the unit cell containing N atoms. Only those signs were accepted whose probability of a correct determination equalled or exceeded 99%. From the original set and the additional 16 signs, 52 additional signs were developed. In the course of the phar:e development, the tendency for C to be negative became overwhelming. Also, several indications developed ~ , ~sign of 802 that “A” was positive. From the g1 r e l a t i ~ n s h i p ,the was determined to be positive with an 89% confidence. Accordingly, a three-dimensional Fourier was computed for which the signs of A and B were positive and that for C was negative. The outline
Table II. Starting Set of Vectors for the Symbolic Addition Phase Determination hkl
+ (Eh) = 2-1 + 2-1 tanh
S
++ + A B C
Table 111. Final Atom Positions and Thermal Parameters‘ Atom 0-1 0-2 0-3 0-4 C-1
C-2 a
X
Y
z
-0.4653 (3) 0.2787 (6) 0.2085 (3) 0.2752 (2) -0 4451 (3) -0.1267 (6) 0.2253 (7) -0.0776(3) -0.2713 (4) -0.2402 (4) -0.1861 (7) -0.0175 (3) -0.4768 (4) 0.0442 (6) 0.1418 (3) 0.0084 (8) -0.0251 (3) -0.3551 (4)
411
R22
0.0088 ( 5 ) 0.0081 ( 5 ) 0.0146 (6) 0.0095 ( 6 ) 0.0057 ( 5 ) 0.0065 (6)
0.0263 (11) 0.0369 (12) 0.0519 (16) 0.0599 (18) 0.0256 (13) 0.0326 (14)
Thermal parameters are of the form T,,,,I{ -(@llh2
Riz
433
0.0136 ( 5 ) -0.0012 ( 5 ) 0.0102 ( 5 ) O.oo00 ( 5 ) 0.0066 (4) -0.0167 (8) 0.0133 (7) 0.0076 ( 5 ) 0.0071 ( 5 ) -0.0003 (6) 0.0066 ( 5 ) -0.ooO6 (7)
a13
423
-0.0017 (3) -0,0044 ( 5 ) -0.0011 (3) 0.0050 ( 5 ) 0.0009 (3) -0.0013 ( 5 ) -0.0012 (3) -0.0058 ( 6 ) 0,0000 (3) -0.0014 ( 5 ) 0.0000 (4) -0.0015 (6)
+ &kZ + P d 2 + 2&hk + 2/313hl + 2&3kl,].
Experimental Section Diketocyclobutenediol, “squaric acid,” was synthesized by Dr. Wayne C. Solomon according to the method of Cohen, Lacher, and Park.3 The conversion of squaric acid to octahydroxycyclobutane was accomplished after the method described by West, Niu, and 1to.I Attempts at recrystallization at ambient conditions from aqueous solutions yielded only several poor crystals from a frothy mass of decomposed material. The crystals used in this study were cut from clear, colorless, diamond-shaped crystals grown by slow evaporation from an aqueous solution in a refrigerator. Space group data were obtained from Weissenberg camera photographs. Intensity data were gathered using a General Electric XRD-5 single crystal orienter equipped with a scintillation counter and a pulse height analyzer. Nickel-filtered copper radiation (A 1.54178) was used for both lattice parameter measurements and the taking of the intensity record. Lattice parameters reported here were taken at a 1 ” take-off angle on high 8 inflections showing ~ - C Y Z splitting. The intensity record was taken at a take-off angle of 3” using a n open counter and the 8-28 scan technique, The crystal used was an approximately square prism 0.2 X 0.2 X 0.5 mm. Crystal Data. Octahydroxycyclobutane crystallizes in the monoclinic space group P21/n. Crystal d!ta areao = 7.525 + 0.005, bo = 5.472 f 0.005, CO = 7.491 h 0.005 A; p = 90.00 f 0.05’; Pabad = 2.00, Pesled = 1.98; two molecules [C4(OH)s] in the unit cell. With two molecules per cell, the molecules are required to lie on centers of symmetry, and therefore the cyclobutane ring must be planar. Solution of the Structure. After initial Lorentz and polarization correction, the intensity data were converted to normalized structure factorsa4 Statistical data derived from the distribution of E‘s are presented in Table I. The symbolic addition method of Karle and Karle5 was used to determine phase relationships. The starting set of origin-fixing vectors is listed in Table 11. Also listed in Table I1 are the vectors for which symbolic signs were used in the uz relationship. The u26 method consists of the application of the relationship (3) S. Cohen, J. R. Lacher, and J. D. Park, J . Am. Chem. Soc., 81, 3480 (1959). (4) H. Hauptman and J. Karle, “Solution of the Phase Problem I, the Centrosymmetric Crystal,” American Crystallographic Association, Monograph No. 3, Polycrystal Book Service, Pittsburgh, Pa., 1953. (5) I. L.Karle and J. Karle, Acta Cryst., 16, 969 (1963).
of the molecule was easily recognized from the Fourier, and atom positions were entered directly into a least-squares refinements allowing atom x , y , z positions, one over-all temperature, and one over-all scale factor as variables. The conventional R factor for nonzero observed data rapidly fell to 20%, whereupon the atoms were allowed to assume individual isotropic thermal motion. The refinement of the structure rapidly converged to the rather high discrepancy index of R = 19.0% for nonzero observed data. The reason for the high discrepancy index at this point is interpreted as a manifestation of the highly anisotropic thermal motion of the oxygen atoms. Introduction of a weighting schemeg of the form
where a = 2/F0,minand c = 2/Fu,,,,axand anisotropic thermal motion rapidly brought the R factor for nonzero observed data to 10.1 %. R for all data is 14%. At this point, a difference Fourier was calculated; however, no features could be unequivocally identified as the missing hydrogen atoms and the refinement was therefore terminated. The failure of the difference Fourier to locate the hydrogen atoms may be because of the magnitude of thermal motion of the oxygen atoms coupled with the usual random error in the observed intensity data.10 Low angle reflections which are apparently affected by extinction were weighted as zero in the final refinement. Omission of these reflections from the usual discrepancy index, R, yields 7.2 % for nonzero observed data and 11.5 % for all data. Final atom positions and thermal parameters are listed in Table 111. (6) M. M.Woolfson, ibid., 7, 61 (1954). (7) I. L. Karle, K. Britts, and S. Brenner, ibid.,17, 1506 (1964). (8) W. R. Busing, K. 0. Martin, and H. A. Levy, “ORFLS,” Oak Ridge National Laboratory, Oak Ridge, Tenn., 1962. (9) D. W.J. Cruickshank, “Computing Methods in Crystallography,” J. S. Rollett, Ed., Pergamon Press, New York, N. Y., 1965, p 114. (10) Observed and calculated structure factors have been deposited as Document No. 9651 with the AD1 Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington, D. C. A copy may be secured by citing the document number and by remitting $1.50 for photoprints, or $1.25 for 35-mm microfilm. Advance payment is required. Make checks or money orders payable to: Chief, Photoduplication Service, Library of Congress. Bock
/
Structure of Octahydroxycyclobutane
2750
Figure 1.
Stereodiagram of the molecular structure of octahydroxycyclobutane.
Discussion The configuration of the molecular structure and its packing arrangement are shown in the stereodiagrams in Figures 1 and 2. These diagrams were drawn with the aid of the computer program ORTEP.” Important interatomic distances and angles and their estimated standard errors were calculated with the program OR FEE'^ and are listed in Table IV. As expected, difference calculations among the carbon-oxygen bond lengths showed that the bonds are all equivalent within the error of the experiment. In this respect, the author prefers to use the philosophy of Hamiltonl3 in that estimates of precision should be doubled before statistical inferences are made from the data, The average C-0 bond of 1.385 k is consider5bly shorter than the normal paraffinic bond of 1.43 A.14 (11) C. K. Johnson, “ORTEP,” Oak Ridge National Laboratory Report 3794, Oak Ridge, Tenn., 1965. (12) W. R. Busing, K. 0. Martin, and H. A. Levy, “ORFEE,” Oak Ridge National Laboratory Report 306, Oak Ridge, Tenn., 1964. (13) W. C. Hamilton, “Transactions of the American Crystallographic Association,” Vol. 1, S. C. Abrahms, Ed., Polycrystal Book Service, Pittsburgh, Pa., 1965.
Journal of the American Chemical Society / 90:11
Owen and Hoard15 observed a similar shortening of the C-Cl bond in octachlorocyclobutane over the normal C-C1 single boad, and a similar shortening of a C-0 bond to 1.39 A was observed by Brown and LevyI6 in chloral hydrate wherein two hydroxyls are also bonded to a single carbon atom. The difference between the angles 01-C1-02 and Oz-Cz-04 is apparently significant ; however, this apparent difference may be due to inaccuracies in error estimation of the lack of consideration of the effect of thermal motion on bond angles and distances. The observed carbon-carbon bond lengths of 1.562 and 1.564 k are in excellent agreement with the 1.56-A distance measured in cyclobutane by electron diffraction,” but it is shorter than the 1.59-A distance observed in octachlorocyclobutane. l 5 The planarity of the ring for the hydroxyl compound may be because of the (14) “International Tables for X-Ray Crystallography,” Vol. 111, K. Lonsdale, Ed., The Kynoch Press, Birmingham, England, 1962, p 202. (15) T. B. Owens and J. L. Hoard, Acta Cryst., 4, 172 (1964). (16) G. M. Brown and H. A. Levy, J. Phys. Radium, 25, 469 (1964). (17) J. D.Dunitz and V. Shoemaker, J. Chem. Phys., 20, 1703 (1952).
1 May 22, 1968
2751
Table IV. Bond Distances and Angles for Octahydroxycyclobutane~ Bond distance, 8,
Atoms C1-G
1.564 1.562 1.380 1.390 1.400 1.372
c1-c2 c1-01 c1-02
-3
Bond angle, deg
H bond, 8,
-f 0.004
f 0.004 -f 0.005 f 0.004 f 0.005 f 0.005
c2-04
-
Mean C-0
1.385 110.8 112.7 89.8 90.2
=k 0 . 3 dz 0 . 3 -f 0 . 2 f 0.2
2.790 2.806 2.897 2.905 2.806 2.905 2.790 2.897 Mean 0 . . . O
f 0.004 f 0.004 0.004 f 0.004 z!= 0.004 =t 0.004
2.850
Asymmetric unit I at
I1 I11
IV V VI VI1 a
=t 0.004 =t 0.004
X
-1
-x
+x + x 'I2 + x - -x '12
'12
'12
- 112
-
x
Y -Y - 112 y - '12 Y 'I2 - Y - '12 Y '12 Y
++ +
Z -2
- '12 -112
- '12 '12 'I2 -
+- zz +z z
z
All distances less than 4 8, were computed, but only significant approaches are listed.
hydrogen-bonding scheme. The fact that octafluorocyclobutane has a nonplanar ringl8 $nd that the oxygen and fluorine radii at 0.64 and 0.66 A,19respectively, are essentially the same size would seem to rule out crowding as a cause of ring warping. One referee pointed out that it is possible that a statistically nonplanar ring could satisfy these data. To test the hypothesis that a statistically disordered nonplanar ring could better explain the observed data, a split atom refinement was attempJed. Atoms of halfweight were offset along bo f0.2 A from their positions as listed in Table IV. After three full cycles of anisotropic least-squares full-matrix refinement varying three positional parameters and six thermal parameters per atom for alternate half-atoms, the residual for nonzero observed F data converged on a minimum of 0.097. According to Hamilton,*O for the split atom refinement to have been significantly better than the ordered model at the 95 confidence level, the residual would have had to have been 0.092 or smaller. The hypothesis that a disordered warped ring can better explain the diffraction data is, therefore, rejected. (18) H. P. Lemoire and R. L. Livingston, J . Am. Chem. Soc., 74, 5732 (1952). (19) F. A. Cotton and G. Wilkinson, "Advanced Inorganic Chemistry," Interscience Publishers, Inc., New York, N. Y . , 1962, p 93. (20) W. C. Hamilton, "Statistics in Physical Science," The Ronald Press Co., New York, N. Y . , 1964, p 157.
However, it should also be noted that the disordered model refinement does not rule out the possibility that statistically disordered skewed rings are present in the structure. Perhaps a structure determination at lower temperatures would resolve the problem ; however, such an investigation is not currently within the capability of this laboratory. The crystal structure is loosely held together by a three-dimensional network of hydrogen bonds involving all the hydroxyls in the structure. According to Pimente1 and McoClellan, the average hydrogen bond length o,f 2.85 A compares well with the average 2.74 f 0.1 1 A of alcohols. Acknowledgments. The author wishes to express his appreciation to Mr. C . D. Parker of Computing and Software, Inc., who converted many of the programs from other laboratories for use on our IBM 7040. The author is indebted to Dr. Wayne C. Solomon of this laboratory for suggesting this study and for his continuing interest in the problem, and to Dr. Harry M. Nelson of this laboratory for reading the manuscript and making helpful criticisms. This work was accomplished as part of an in-house project of the Propellant Division, Air Force Rocket Propulsion Laboratory. (21) G. C. Pimentel and A. L. McClellan, "The Hydrogen Bond," W. H. Freeman and Co., San Francisco, Calif., 1960, p 284.
Bock
Structure of Octahydroxycyclobutane
